(I'm reading Pearl's Causality right now)

I would expect there to be pretty much none, but I only glanced at the homotopy paper; Pearl talks about equivalences between some models (i.e. they give rise to the same probability distribution, so can't be distinguished by purely observational data), and talks about how you can manipulate a graph to get another equivalent graph (reversing arrows under some conditions etc.), but the rules are much more specific that those I saw in the homotopy paper. For example, the substructure A -> B <- C is treated very differently from the substructure A <- B -> C, and I don't expect that kind of assymetry in homotopy/homology (I may be wrong! I only skimmed it!)